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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 333200.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333200.cc1 | 333200cc2 | \([0, -1, 0, -130164008, -589975833488]\) | \(-32391289681150609/1228250000000\) | \(-9248152592000000000000000\) | \([]\) | \(52254720\) | \(3.5606\) | |
| 333200.cc2 | 333200cc1 | \([0, -1, 0, 7819992, -2615577488]\) | \(7023836099951/4456448000\) | \(-33554985648128000000000\) | \([]\) | \(17418240\) | \(3.0113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333200.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 333200.cc do not have complex multiplication.Modular form 333200.2.a.cc
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
